The following Interactive Activity provides you with some base four blocks you can use to visualize place value in base four operations. The pieces are called flats, longs, and units, and they represent 42, 41, and 40, respectively. Use the blocks to solve Problem C6.

Remember that there are four digits in base four (0 through 3). For addition problems, every time you have four blocks of the same type (a given place value), you need to trade them (or regroup them) for one block of the next-larger place value on the left. So, for example, four blocks representing 40 (four units) would be traded for one block representing 41 (one long). Use the regroup button in the activity to do this.

Similarly, for subtraction, every time you don't have enough blocks in a given place value to do the subtraction, you need to take one larger block from the place value on the left and trade it for four blocks of the next-smaller place value on the right. So, for example, one block representing 41 (one long) can be traded for four blocks representing 40 (four units). Use the regroup button in the activity to do this. Note 3

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For a non-interactive version of this activity, print and cut out several base four blocks PDF to use with Problem C6.

Problem C6

Complete the following calculations of these base four numbers:

a.

33four + 11four

b.

123four + 22four

c.

223four - 131four

d.

112four - 331four

Video SegmentWhy is computing in different bases useful? In this segment, Mr. Glasgow and Mr. Marable explain how today's computer technology relies on base sixteen numbers in order to compress complex computer operations.

Can you make a prediction about what number systems computers will use in the future?

If you are using a VCR, you can find the first part of this segment on the session video approximately 22 minutes and 24 seconds after the Annenberg Media logo. The second part begins approximately 25 minutes and 14 seconds after the Annenberg Media logo.